Question

On a certain "anticurl" operator

score 111 · Answer 1 · 2023-03-03 17:55:16

111

Views

On a certain "anticurl" operator

Published on 03 Mar 2023 - 17:55

score 25 · Answer 2 · 2023-03-13 07:47:17

25

Views

A vector field $V$ is gradient of some function $f$ on an open rectangular solid in $\mathbb{R}^3$

Published on 13 Mar 2023 - 7:47

score 299 · Answer 3 · 2023-03-17 11:35:33

299

Views

What is the vorticity of a velocity field?

Published on 17 Mar 2023 - 11:35

score 45 · Answer 4 · 2023-04-21 22:08:16

45

Views

How are the formal definitions of curl interpreted? Where do they appear from and how to derive them?

Published on 21 Apr 2023 - 22:08

score 30 · Answer 5 · 2023-04-26 03:30:37

30

Views

Dot product symbol for divergence, merely a convenience?

Published on 26 Apr 2023 - 3:30

score 118 · Answer 6 · 2023-04-28 11:38:38

118

Views

Why can the del operator cross product a triple integral be placed inside the triple integral?

Published on 28 Apr 2023 - 11:38

score 330 · Answer 7 · 2026-02-23 08:22:58

330

Views

Why is curl given by a cross product?

Published on 23 Feb 2026 - 8:22

score 91 · Answer 8 · 2023-05-25 23:47:25

91

Views

Stokes theorem applied to planes

Published on 25 May 2023 - 23:47

score 153 · Answer 9 · 2023-06-02 16:31:44

153

Views

Integration using Stokes' theorem

Published on 02 Jun 2023 - 16:31

score 125 · Answer 10 · 2023-06-02 18:43:51

125

Views

Find an irrotational function $F(x)$ and a solenoidal function $G(x)$ such that $H = F + G$.

Published on 02 Jun 2023 - 18:43

score 224 · Answer 11 · 2023-06-08 07:31:11

224

Views

Prove that $\bar{F} = r^n \bar{r}$ is conservative and find the scalar potential $\phi$ such that $F = grad\,\phi$.

Published on 08 Jun 2023 - 7:31

score 186 · Answer 12 · 2023-06-08 18:57:58

186

Views

If $\bar{F}=(xyz)^b (x^ai + y^aj + z^ak)$ be irrotational, then show that $b=0$ or $a=-1$. Find the scalar potential $\phi$.

Published on 08 Jun 2023 - 18:57

score 64 · Answer 13 · 2026-02-23 10:06:00

64

Views

If $\vec F=\frac{\vec r}{r^3}$ then $\exists$ is no $\vec G ∶ \mathbb{R}^3 ⧵ {0} \to \mathbb{R}^3$ such that $\vec F = curl \,\vec G$.

Published on 23 Feb 2026 - 10:06

score 24 · Answer 14 · 2023-06-12 19:32:50

24

Views

Is $(f_1(x)+f_2(y)+f_3(z))\vec{r}$ irrotational?

Published on 12 Jun 2023 - 19:32

score 67 · Answer 15 · 2023-06-14 13:28:33

67

Views

Show that $\nabla\cdot [(\vec u\times \vec v)\times \vec w]=\vec w\cdot [(\vec v\cdot \nabla)\vec u-(\vec u\cdot \nabla)\vec v]$

Published on 14 Jun 2023 - 13:28

List Question

On a certain "anticurl" operator

A vector field $V$ is gradient of some function $f$ on an open rectangular solid in $\mathbb{R}^3$

What is the vorticity of a velocity field?

How are the formal definitions of curl interpreted? Where do they appear from and how to derive them?

Dot product symbol for divergence, merely a convenience?

Why can the del operator cross product a triple integral be placed inside the triple integral?

Why is curl given by a cross product?

Stokes theorem applied to planes

Integration using Stokes' theorem

Find an irrotational function $F(x)$ and a solenoidal function $G(x)$ such that $H = F + G$.

Prove that $\bar{F} = r^n \bar{r}$ is conservative and find the scalar potential $\phi$ such that $F = grad\,\phi$.

If $\bar{F}=(xyz)^b (x^ai + y^aj + z^ak)$ be irrotational, then show that $b=0$ or $a=-1$. Find the scalar potential $\phi$.

If $\vec F=\frac{\vec r}{r^3}$ then $\exists$ is no $\vec G ∶ \mathbb{R}^3 ⧵ {0} \to \mathbb{R}^3$ such that $\vec F = curl \,\vec G$.

Is $(f_1(x)+f_2(y)+f_3(z))\vec{r}$ irrotational?

Show that $\nabla\cdot [(\vec u\times \vec v)\times \vec w]=\vec w\cdot [(\vec v\cdot \nabla)\vec u-(\vec u\cdot \nabla)\vec v]$

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